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Creators/Authors contains: "Pina, Andi"

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  1. Quantum Information Science and Engineering (QISE) is rapidly gaining interest across a wide range of disciplines. As QISE continues to evolve, engineering will play an increasingly critical role in advancing quantum technologies. While efforts to characterize introductory QISE courses are underway, a comprehensive understanding of QISE education across the United States remains lacking. Developing a broad understanding of the QISE education landscape is crucial for addressing the needs of the growing quantum industry and ensuring equitable access for a diverse range of participants. This paper presents part of an ongoing effort to characterize the current landscape of QISE courses and degree programs in higher education in the US. To achieve this, we used publicly available information from university and college websites to capture information on over 8000 courses that address quantum in some way and nearly 90 QISE specific programs (e.g., degrees, minors, certificates). The majority of these programs are interdisciplinary and include engineering; 14 of them are housed exclusively in engineering departments. We find most programs are offered at research intensive institutions. Our results showcase an opportunity for program developers at non-research intensive institutions to justify the creation of QISE programs, which would also address calls from different stakeholders in QISE education for a more diverse QISE workforce. We suggest strategies based on the findings of this study such as integrating QISE into existing courses, investing in the development of QISE courses and programs at non-PhD-granting institutions, and making courses with QISE content accessible to students from a variety of majors. 
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    Free, publicly-accessible full text available June 1, 2026
  2. Abstract This work investigates how students interpret various eigenequations in different contexts for$$2 \times 2$$ 2 × 2 matrices:$$A\vec {x}=\lambda \vec {x}$$ A x = λ x in mathematics and either$$\hat{S}_x| + \rangle _x=\frac{\hbar }{2}| + \rangle _x$$ S ^ x | + x = ħ 2 | + x or$$\hat{S}_z| + \rangle =\frac{\hbar }{2}| + \rangle$$ S ^ z | + = ħ 2 | + in quantum mechanics. Data were collected from two sources in a senior-level quantum mechanics course; one is video, transcript and written work of individual, semi-structured interviews; the second is written work from the same course three years later. We found two principal ways in which students reasoned about the equal sign within the mathematics eigenequation and at times within the quantum mechanical eigenequations: with a functional interpretation and/or a relational interpretation. Second, we found three distinct ways in which students explained how they made sense of the physical meaning conveyed by the quantum mechanical eigenequations: via a measurement interpretation, potential measurement interpretation, or correspondence interpretation of the equation. Finally, we present two themes that emerged in the ways that students compared the different eigenequations: attention to form and attention to conceptual (in)compatibility. These findings are discussed in relation to relevant literature, and their instructional implications are also explored. 
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